Mathematics of AC Voltages
Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage v can be described mathematically as a function of time by the following equation:
- ,
where
- is the peak voltage (unit: volt),
- is the angular frequency (unit: radians per second)
- The angular frequency is related to the physical frequency, (unit = hertz), which represents the number of cycles per second, by the equation .
- is the time (unit: second).
The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of is +1 and the minimum value is −1, an AC voltage swings between and . The peak-to-peak voltage, usually written as or, is therefore .
Read more about this topic: Alternating Current
Famous quotes containing the word mathematics:
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)